Static and Seismic Response of Deep Spherical Cavities

An analytical solution is derived for a supported deep spherical cavity, and for the following scenarios: static loading with far-field vertical and horizontal stress, with the ground either dry or saturated with flow or no flow towards the cavity, and seismic loading for drained and undrained loading conditions. The solutions are obtained with the assumption that the ground and the support are elastic and remain elastic during loading, for tied ground-liner interface, excavation and liner support occur at the same time, the liner is thin and its response can be approximated as that of a membrane and the seismic demand can be represented as a far-field static shear stress. The correctness of the analytical solution is verified by comparing its results with those of the finite element code ABAQUS. Inspection of the closed-form solutions shows that the static response of the cavity strongly depends on the relative stiffness of the support relative to the ground and on the coefficient of earth pressure at rest. In addition, the seismic response also depends on the type of loading, either drained or undrained. Results from the seismic analysis show that undrained loading results in larger stresses in stiffer liners, while drained loading imposes larger displacements in flexible liners.